Asymptotic iteration method for the inverse power potentials

The asymptotic iteration method (AIM) is used to accurately calculate the eigenvalues of the Schrödinger equation with the potential 𝑉(𝑟)=−𝑟−𝑠, 𝑠∈(0,1), in arbitrary dimensions. The recently studied case, 𝑠=1/2, is discussed in detail where we give a reason for non-polynomial solutions. Using AIM sequences, we develop a method to compute the coefficients of the series solution in this case. AIM applications for 𝑠=1/3,𝑠=1/4 and 𝑠=2/3 are also discussed.